1. Field of the Invention
The invention relates to a method for determining the position and rotational position of an object in three-dimensional space.
The objects suitable for the invention are varied and are very different in their function and application. Examples of such objects are surgical microscopes and surgical tools in the medical sector, levelling staffs in geodetic surveying, gun barrels in the military sector or aerials, in particular directional aerials and radar aerials. In the case of such objects, their position in space plays an important role. This is determined in a specified coordinate system completely by six real position parameters which are composed of three parameters for the position (translation group) and three parameters for the rotational position (rotation group). The position of the object is given by the 3-dimensional coordinates of a point selected on the object. The rotational position of the object is generally described by the direction vector of a defined object axis and the angle of rotation of the object about the object axis. The direction vector of the object axis is a unit vector having the length 1, i.e. the sum of the squares of its components is 1.
2. Description of the Background Art
WO 95/27918 describes an arrangement for determining the spatial position of a surgical microscope with the aid of coded light signals which are emitted by light emitting diodes, preferably in the infrared range, and received by light receivers. A surgical microscope is generally mounted on an arm by means of a cardan joint and can be moved translationally in three directions in space and rotated about three directions in space so that its position in space can be adjusted as desired. On the surgical microscope, the light emitting diodes or optical fibres which are fed with light from the light emitting diodes are mounted at specific points. Alternatively, reflectors may also be mounted on the surgical microscope. The light receivers are arranged at various points in space and receive the light signals specific to each of them. From this, the spatial position of the surgical microscope is determined. If the spatial position of the patient is simultaneously known, the coordinates of the operating site viewed through the surgical microscope are thus known, which is indispensable for microsurgery.
In geodetic surveying, levelling staffs are used for determining vertical points of reference and for topographical surveying. They are also used in construction surveying and in the construction of traffic routes. A levelling staff is sighted with the telescope optical system of the levelling instrument in order to measure the difference in height between levelling instrument and levelling staff. It is assumed that the levelling staff is aligned perpendicular to the optical axis of the telescope. Since the optical axis of the telescope is usually adjusted so that it is in a horizontal plane, an operator must keep the levelling staff aligned as far as possible perpendicular with the aid of the water levels mounted thereon. Tilting of the levelling staff results in an error in the height measurement.
With the advent of automated digital levelling instruments according to DE 34 24 806 C2, electronic reading of the staff became possible for the first time. For this purpose, the levelling staff has a code pattern comprising black and white elements, a part of which is produced as an image on a position-resolving detector with the aid of the telescope optical system of the electronic levelling instrument. Here, the code pattern information present in the field of view of the telescope is used to obtain the desired height measurement by comparison with the code pattern of the levelling staff, which pattern is stored as a reference code pattern in the levelling instrument. Although the measured code pattern is identified in this measurement and evaluation method, tilting of the levelling staff and the resulting contribution to the inaccuracy of measurement are not taken into account.
A specific code pattern is disclosed in DE 195 30 788 C1. A levelling staff having a rotationally symmetrical cross-section has, on its lateral surface, code elements which form lines closed rotationally symmetrically with respect to the longitudinal axis of the levelling staff. Consequently, the code pattern is visible from all sides.
DE 44 38 759 C1 describes a method for determining the tilt angle of coded levelling staffs in the measuring direction by means of an electronic levelling instrument. The tilt of the levelling staff is taken into account exclusively in the measuring direction, i.e. in the observation direction. The resulting recording of the code pattern on the detector is evaluated and the tilt angle is determined. Lateral tilting of the levelling staff, which thus takes place transversely to the observation direction of the levelling instrument, is however not taken into account. A one-dimensional diode array is therefore adequate as a detector.
Owing to a lateral tilt of the levelling staff, an error also occurs in the height and distance measurement. The point of intersection of the optical axis of the levelling instrument with a tilted levelling staff is further away from the bottom of the levelling staff than in the case of exactly perpendicular alignment of the levelling staff. An insufficiently perpendicular alignment due to inaccurate reading of the water level by the operator therefore leads to erroneous measurements. There is subsequently no possibility for correcting errors. Moreover, often only a single operator is used today, said operator operating the levelling instrument for surveying. The levelling staff standing alone is exposed to the wind, which leads to corresponding deviations in the surveying.
In the case of a gun barrelxe2x80x94and the following statement also applies analogously in the case of directional aerials and radar aerialsxe2x80x94the primary concern is to determine its orientation in space or to rotate the gun barrel into a specific predetermined direction and to measure said rotation. The horizontal and vertical angular position (azimuth and elevation) of the gun barrel is controlled with the aid of encoders which are mechanically connected to the gun barrel. The encoders contain in general coded rotary discs which execute a rotational movement by means of a gear during rotation of the gun barrel and thus deliver electrical signals corresponding to the angles of rotation. The mechanical play is disadvantageous in the case of such controls. Moreover, the large thermal loads and shocks lead to inaccuracies and to increased wear.
It is the object of the invention to provide a method by means of which the position and the rotational position of an object in three-dimensional space can be determined quickly and without contact.
The object is achieved, according to the invention, by use of an optical measuring head including an imaging optical system and a detector which is position-resolving in two dimensions and is arranged in the focal plane of the imaging optical system. The object with its object structures is focused onto the detector by the imaging optical system. The object structures are known from the outset as a priori information. The object structures may contain the geometric shape of the object and its dimensions or may be marks at specific points on the object or they may be a code pattern which is applied to the object. The image of the object or of the object structures which is present in two-dimensional form on the detector is evaluated in an evaluation unit connected to the detector.
There are various possibilities for evaluating the two-dimensional image information. For example, the image of the object can be compared with calculated images. From the known geometry of the object or from existing marks on the object or from an existing code pattern on the object or from all these object structures together, the expected detector image can be calculated using the known properties of the imaging optical system (and optionally the resolution of the position-resolving detector) for any reasonable values of the six position parameters stated at the outset. Optimization methods are used for determining those values of the position parameters which give the best or at least a sufficiently good agreement between the calculated image and the image actually recorded. Such optimization methods are, for example, quasi-Newton methods (determination of the least squares or of the maximum likelihood, etc.), which are known from K. Levenberg: xe2x80x9cA Method for the Solution of Certain non-linear Problems in Least Squaresxe2x80x9d, Quart. Apl. Math. 2 (1944), pp. 164-168, or from D. W. Marquardt: xe2x80x9cAn Algorithm for Least-squares Estimation of Nonlinear Parametersxe2x80x9d, SIAM J. Appl. Math. 11 (1963), pp. 431-441, or from J. J. Morxc3xa9: xe2x80x9cThe Levenberg-Marquardt Algorithm: Implementation and Theoryxe2x80x9d, Numerical Analysis, ed. G. A. Watson, Lecture Notes in Mathematics 630, Springer Verlag (1978), pp. 105-116.
Another possibility for evaluation is to analyze the object structures focused on the detector with respect to their geometrical parameters and to determine the position parameters of the object therefrom. Thus, the planar position and the rotational position of the focused geometrical shapes (e.g. edge contours) or of the code pattern on the detector and the variation in the image scale changing as a function of the detector coordinates are first measured and determined. If a code pattern is present, all code elements of the code pattern focused on the detector are preferably completely used since high accuracy and especially high ruggedness and stability of the evaluation result can thus be achieved. For other requirements, such as, for example, for particularly rapid availability of the results of the measurement, however, the evaluation of only three decoded code elements of the code pattern is sufficient. The accuracy of the measurement is somewhat limited. Alternatively, it is also possible to evaluate only the focused edge contours of the object.
From the determined geometrical parameters of the detected object structures, the position parameters of the object are determined with the aid of the optical imaging equation and geometrical relationships (vector algebra). By means of the position parameters, which as mentioned at the outset include the position vector, the direction vector of the object axis and the angle of rotation of the object about the object axis, the spatial position of the object, i.e. the position and rotational position, is reconstructed.
Of course, said possibilities for evaluation can also be combined with one another. For example, a rough determination of the position parameters can be effected by a rough evaluation of the edge contours or of only a few code elements and an accurate evaluation including the total recorded object geometry or all recorded code elements can follow. For the accurate evaluation, in particular the optimization method cited above can also be used and the position parameters determined from the rough evaluation can be employed as starting parameters for the optimization.
Expediently, a three-dimensional Cartesian coordinate system is chosen for determining the spatial position of the object. The coordinates of the measuring head and hence of the detector are known in this coordinate system. The coordinate system may also be chosen from the outset so that it agrees with the detector coordinates. Of course, the position parameters of the object can be converted into any desired expedient coordinate system. In particular, the rotational position of the object may also be specified by two polar angles or by azimuth, elevation and in each case the angle of rotation of the object about the axis of rotation or by three Eulerian angles.
An optoelectronic detector capable of position resolution in two dimensions is required for the invention. Said detector may be, for example, a video camera or two-dimensional CCD array. However, it is also possible to use a plurality of one-dimensional CCD arrays arranged side by side. The object is mapped with such a detector and by means of the imaging optical system. The object structures present in the field of view of the imaging optical system are focused and detected. The detector is adjusted with its light-sensitive detector surface generally perpendicular to the optical axis of the imaging optical system. The point of intersection of the optical axis with the light-sensitive detector surface may define the zero point of the coordinate system of the detector.
When a CCD detector having discrete light-sensitive pixel structures is used, the positional resolution of the CCD detector can be further considerably increased by means of suitable optic structures, in particular by means of suitable structures of a code pattern. More than 10 times the pixel resolution of the detector is thus achievable. The particular measurement sensitivity is obtained if the fundamental spatial frequency or one of the higher harmonic spatial frequencies of the intensity distribution caused by the code pattern on the detector forms a low-frequency superposition pattern together with the fundamental spatial frequency of the radiation-sensitive structures of the detector. The low-frequency superposition pattern acts in the same way as a moirxc3xa9pattern. Moirxc3xa9 patterns are known to be very sensitive to a shift in the structures which produce them. Here, this means that, even in the case of a very small change in the intensity distribution on the detector compared with its pixel structure, the low-frequency superposition pattern changes considerably in its spatial frequency. Thus, the position of the focused code pattern on the detector can be measured very precisely. Since a change in the superposition pattern is caused by a change in the position and rotational position of the object, the position parameters of the object in space can therefore be measured in a very sensitive and hence highly precise manner.
If the object is a levelling staff, the direction vector of its axis is also important in addition to its position, since said vector describes the tilt of the levelling staff from the perpendicular. In addition to the known conventional levelling staffs where a code pattern is applied to a flat surface, it is also possible to use a levelling staff which is rotationally symmetrical with respect to its longitudinal axis and has a rotationally symmetrical bar code. In this case, the imaging optical system can pick up the same code pattern even continuously from all sides of the levelling staff. By determining the direction vector of the levelling staff axis from the focused code pattern or the detected contours of the levelling staff, both the inclination of the levelling staff in the direction of view of the imaging optical system and the lateral inclination of the levelling staff transverse to the direction of view of the imaging optical system are determined. Thus, the deviation of the levelling staff from the ideal perpendicular is determined and is taken into account in a corresponding correction for the surveying. This correction is made automatically in every survey. Consequently, it is even possible to dispense with prior alignment of the levelling staff. As a result, fast and precise surveying with only a single operator and also independently of the wind conditions is possible. If moreover, in the given case, the angle of rotation of the levelling staff about its axis is also determinedxe2x80x94assuming a suitable code pattern or specific marksxe2x80x94this automatically also gives the sighting direction of a movable measuring head.
If the object is a gun barrel, this can be equipped with various code patterns, analogously to the case of the levelling staff. If only elevation and azimuth of the gun barrel are to be determined, a code pattern rotationally symmetrical with respect to the longitudinal axis of the gun barrel or only the edge contour of the gun barrel is sufficient. If a code pattern comprising code lines aligned parallel to the longitudinal axis is additionally applied to the gun barrel, its angle of rotation about its axis can additionally be determined. The code lines may also be stochastically oriented. Combinations of these code patterns in which, for example, segments having rotationally symmetrical code rings and segments having parallel or stochastic code lines alternate can also be used. A code pattern which is wound in a spiral manner around the gun barrel and with which about the same sensitivity for the direction vector of the gun barrel axis and the angle of rotation of the gun barrel about its axis can be achieved is also advantageous. However, it is also possible to use a code pattern having a completely irregular structure, as possessed, for example, by military camouflage patterns. What is decisive for all code patterns is that they are either known per se or are determined by surveying. Advantageously, such code patterns can be readily used for the correlation procedures.
By means of the imaging optical system, the contours of the gun barrel and/or of the code pattern are recorded and the rotational position of the gun barrel is determined without contact. Optionally, the gun barrel can be actively illuminated, for example with infrared light. The gun barrel or the applied code pattern may also be luminescent. Generally firm locking of imaging optical system and detector relative to the gun barrel and the optical surveying result in the great advantage that absolutely no mechanically moving components are required for determining azimuth, elevation and angle of rotation of the gun barrel. This contactless measurement takes place rapidly and gives precise results.
If the object is an aid used in the medical environment, in particular in automated microsurgery, such as, for example, a surgical microscope, a surgical tool (scalpel, drill, endoscopic aid, etc.) or a radiation source for tumour treatment, good visibility of the object structures of the aid must be ensured for the measuring head. During handling of the aid, the latter may be temporarily concealed by persons or instruments and the direction of view of the measuring head interrupted. However, if it is intended constantly to measure the spatial position of the aid under these conditions, it is useful if the object structures to be detected by the measuring head are located in an exposed area of the aid so that they are as far as possible in the unobstructed direction of view of the measuring head. When a code pattern is used, it may also be applied to a plurality of points on the aid or it may even cover the entire surface of the aid. The measuring head may be movable in space for an optimal recording, or preferably a plurality of measuring heads distributed in space are used simultaneously. The redundancy of the results delivered by a plurality of measuring heads moreover meets the requirement set in the medical sector for particular equipment safety.
Otherwise, the object may also be the patient itself, i.e. more precisely a frame which is firmly connected to the patient and defines the coordinate system of the patient. Precisely in operations on tumours in the brain, such a frame is fixed to the patient""s head, the spatial position of the tumour relative to the frame being determined, for example, by computed tomography images. If the geometric structures of the frame or the code patterns applied to the frame are recorded by the measuring heads and the spatial position of the frame is determined, the coordinates of the tumour are also known in the coordinate system of the measuring heads. Since moreover the spatial position of the surgical microscope and of the surgical tool is determined with the aid of the measuring heads, endoscopic navigation through the brain to the tumour can be performed fully automatically.
In all stated application examples of the invention, it is possible that it may be difficult to provide an object with a code pattern to be used or that the object is already present as a complete component. In such cases, it is possible to mount a separate body provided with a code pattern eccentrically on the object (xe2x80x9cbooster principlexe2x80x9d). The body may have a cylindrical shape. It is of course also possible to mount a plurality of such bodies on one object. If the object moves in space, the separately mounted body, too, performs clearly coupled movements, in particular rotational movements so that the position and rotational position of the object can always be computed.
In addition, an object can also be recorded stereoscopically. For this purpose, either two measuring heads can form a stereo base or the stereo base is produced by a measuring head together with a focusing mirror or a plurality of focusing mirrors, so that the measuring head can record stereoscopic images of the object. By means of this additional image information, the accuracy of the position determination of the object can be further increasedxe2x80x94analogously to seeing with two eyes.
Finally, a distance measuring instrument can also be connected to the measuring head or integrated therein. With such additional information about the distance of the object, it is also possible to increase the accuracy of measurement. Moreover, the additional information can ensure that the measured result regarding the position of the object is available more quickly.